Analysis of Diffusion-Controlled Dissolution from Polydisperse Collections of Drug Particles with an Assessed Mathematical Model

Comparative Evaluation of Dissolution Performance in a USP 2 Setup and Alternative Stirrers and Vessel Designs: A Systematic Computational Investigation

The dissolution testing method described in the United States Pharmacopeia (USP) Chapter ⟨711⟩ is widely used for assessing the release of active pharmaceutical ingredients from solid dosage forms. However, extensive use over the years has revealed certain issues, including high experimental intervariability observed in specific formulations and the settling of particles in the dead zone of the vessel. To address these concerns and gain a comprehensive understanding of the hydrodynamic conditions within the USP 2 apparatus, computational fluid dynamic simulations have been employed in this study. The base design employed in this study is the 900 mL USP 2 vessel along with a paddle stirrer at a 50 rpm rotational speed. Additionally, alternative stirrer designs, including the hydrofoil, pitched blade, and Rushton impeller, are investigated. A comparison is also made between a flat-bottom tank and the USP round-bottom vessel of the same volume and diameter. Furthermore, this work examines the impact of various parameters, such as clearance distance (distance between the bottom of the impeller and bottom of the vessel), number of impeller blades, impeller diameter, and impeller attachment angle. The volume-average shear rate (Stv), fluid velocity (Utv), and energy dissipation rates (ϵtv) represent the key properties evaluated in this study. Comparing the USP2 design and systems with the same stirrer but flat-bottom vessel reveals more homogeneous mixing compared to the USP2 design. Analyzing fluid flow streamlines in different designs demonstrates that hydrofoil stirrers generate more suspension or upward movement of fluid compared to paddle stirrers. Therefore, when impellers are of a similar size, hydrofoil designs generate higher fluid velocities in the coning area. Furthermore, the angle of blade attachment to the hub influences the fluid velocity in the coning area in a way that the 60° angle design generates more suspension than the 45° angle design. The findings indicate that the paddle stirrer design leads to a heterogeneous shear rate and velocity distributions within the vessel compared with the other designs, suggesting suboptimal performance. These insights provide valuable guidance for the development of improved in vitro dissolution testing devices, emphasizing the importance of optimized design considerations to minimize hydrodynamic variability, enhance dissolution characterization, and reduce variability in dissolution test results. Ultimately, such advancements hold potential for improving in vitro-in vivo correlations in drug development.

Multifactorial drug carrier system bringing both chemical and physical therapeutics to the treatment of tumor heterogeneity

Tumor heterogeneity and drug resistance have been invincible features of cancer for its complete cure. Despite the advent of immunotherapy, the expansion and diversification of cancer cells evolved even in the absence or presence of drug treatment discourage additional therapeutic interventions. For the eradication of cancer cells, therefore, an 'all-at-once' strategy is required, which exploits both target-selective chemotherapy and non-selective physicotherapy. Multifactorial microcapsules comprising gold nanoparticles (AuNPs) and a self-assembly protein of α-synuclein (αS) were fabricated, in which hydrophobic and hydrophilic drugs could be separately encapsulated by employing lipid-based inverted micelles (IMs). Their combined physico-chemical therapeutic effects were examined since they also contained both membrane-disrupting IMs and heat-generating AuNPs upon irradiation as physicotherapeutic agents. For the optimal enclosure of IMs containing hydrophilic drugs, a porous inner skeleton made of poly(lactic-co-glycolic acid) was introduced, which would play the roles of not only compartmentalizing the internal space but also enhancing proteolytic disintegration of the microcapsules to discharge and stabilize IMs to the outside. In fact, hydrophobic paclitaxel and hydrophilic doxorubicin showed markedly enhanced drug efficacy when delivered in the IM-containing microcapsules exhibiting the 'quantal' release of both drugs into the cells whose integrity could be also affected by the IMs. In addition, the remnants of αS-AuNP microcapsules produced via proteolysis also caused cell death through photothermal effect. The multifactorial microcapsules are therefore considered as a promising anti-cancer drug carrier capable of performing combinatorial selective and non-selective chemical and physical therapies to overcome tumor heterogeneity and drug resistance.

Particle Size, Dose, and Confinement Affect Passive Diffusion Flux through the Membrane Concentration Boundary Layer

The authors present a steady-state-, particle-size-, and dose-dependent dissolution-permeation model that describes particle dissolution within the concentration boundary layer (CBL) adjacent to a semipermeable surface. It is critical to understand how particle size and dose affect the behavior of dissolving particles in the presence of a CBL adjacent to a semipermeable surface both in vivo and in vitro. Control of particle size is ubiquitous in the pharmaceutical industry; however, traditional pharmaceutical assumptions of particle dissolution typically ignore particle dissolution within the length scale of the CBL. The CBL does not physically prevent particles from traveling to the semipermeable surface (mucus, epithelial barrier, synthetic membrane, etc.), and particle dissolution can occur within the CBL thickness (δC) if the particle is sufficiently small (∼dparticle ≤ δC). The total flux (the time rate transport of molecules across the membrane surface per unit area) was chosen as a surrogate parameter for measuring the additional mass generated by particles dissolving within the donor CBL. Mass transfer experiments aimed to measure the total flux of drug using an ultrathin large-area membrane diffusion cell described by Sinko et al. with a silicone-based membrane ( Mol. Pharmaceutics 2020, 17, (7) 2319-2328, DOI: 10.1021/acs.molpharmaceut.0c00040). Suspensions of ibuprofen, a model weak-acid drug, with three different particle-size distributions with average particle diameters of 6.6, 37.4, and 240 μm at multiple doses corresponding to a range of suspension concentrations with dimensionless dose numbers of 2.94, 14.7, 147, and 588 were used to test the model. Experimentally measured total flux across the semipermeable membrane/CBL region agreed with the predictions from the proposed model, and at a range of relatively low suspension concentrations, dependent on the average particle size, there was a measurable effect on the flux due to the difference in δC that formed at the membrane surface. Additionally, the dose-dependent total flux across the membrane was up to 10% higher than the flux predicted by the standard Higuchi-Hiestand dissolution model where the effects of confinement were ignored as described by Wang et al. ( Mol. Pharmaceutics 2012, 9 (5), 1052-1066, DOI: 10.1021/mp2002818).

A new modelling approach for dissolution of polydisperse powders

A new modelling approach for dissolution of polydisperse powders is developed within the framework of the classical Noyes-Whitney/Nernst-Brunner analysis. Its distinguishing feature is that the underlying continuous particle-size distribution is retained. Two different but related dependencies of the diffusion-layer thickness on particle size are considered. First, a power-law dependence that interpolates between a thickness that is proportional to (or equals) the particle radius (obtained when the exponent equals 1) and a constant thickness (obtained when the exponent is 0). Second, a piecewise linear function such that the thickness equals the particle radius for sufficiently small particles and is constant for larger ones. The modelling approach is exemplified by consideration of a lognormal particle-size distribution. Highly accurate closed-form expressions for the fraction of dissolved drug are obtained for dissolution under sink conditions (which are exact if the diffusion-layer thickness is radius-independent). Moreover, it is demonstrated that any result derived under sink conditions can be reused to determine the fraction of dissolved/absorbed drug under non-sink conditions, using the concept of a retarded time. Comparison with literature data and experiments are used to validate the modelling approach and to demonstrate its usefulness in a practical context.

Modeling of Particle Dissolution Behavior Using a Geometrical Phase-Field Approach

Material dissolution is a critical attribute of many products in a wide variety of industries. The idealized view of dissolution through established prediction tools should be reconsidered because the number of new substances with low aqueous solubility is increasing. Due to this, a fundamental understanding of the dissolution process is desired. The aim of this study was to develop a tool to predict crystal dissolution performance based on experimentally measurable physical parameters. A numerical simulation, called the phase-field method, was used to simultaneously solve the time evolution of the phase and concentration fields of dissolving particles. This approach applies to diffusion-limited as well as surface reaction-limited systems. The numerical results were compared to analytical solutions, and the influence of particle shape and interparticle proximity on the dissolution process was numerically investigated. Dissolution behaviors of two different substances were modeled. A diffusion-limited model compound, xylitol, with a high aqueous solubility and a surface reaction-limited model compound, griseofulvin, with a low aqueous solubility were chosen. The results of the simulations demonstrated that phase-field modeling is a powerful approach for predicting the dissolution behaviors of pure crystalline substances.

Characterization of Membrane-Type Dissolution Profiles of Clinically Available Orally Inhaled Products Using a Weibull Fit and a Mechanistic Model

Dissolution rate impacts the absorption rate of poorly soluble inhaled drugs. In vitro dissolution tests that can capture the impact of changes in critical quality attributes of the drug product on in vivo dissolution are important for the development of products containing poorly soluble drugs, as well as modified release formulations. In this study, an extended mathematical model allowing for dissolution of polydisperse powders and subsequent diffusion of dissolved drug across a membrane is described. In vitro dissolution profiles of budesonide, fluticasone propionate, and beclomethasone dipropionate delivered from three commercial drug products were determined using a membrane-type Transwell dissolution test, which consists of a donor and an acceptor compartment separated by a membrane. Subsequently, the profiles were analyzed using the developed mechanistic model and a semi-empirical model based on the Weibull distribution. The two mathematical models provided the same rank order of the performance of the three drug products in terms of dissolution rates, but the rates were significantly different. The faster rate extracted from the mechanistic model is expected to reflect the true dissolution rate of the drug; the Weibull model provides an effective and slower rate that represents not only drug dissolution but also diffusion across the Transwell membrane. In conclusion, the developed extended model provides superior understanding of the dissolution mechanisms in membrane-type (Transwell) dissolution tests.

The Kinetic Aspects of the Dissolution of Slightly Soluble Lanthanoid Carbonates

The problem of the complex use of mineral raw materials is significant in the context of many industries. In the rare earth industry, in the context of limited traditional domestic reserves and dependence on imports of lanthanides, an unambiguous and comprehensive solution has not yet been developed. Promising areas include the involvement of technogenic raw materials in the industrial turnover. The present study examines the kinetics of the dissolution process of poorly soluble lanthanide compounds when changing the parameters of the system. The results obtained reflect the dependence of the degree of extraction of lanthanide on the following variable parameters of the system: temperature, concentration of the complexing agent, and intensity of mixing. On the basis of the experiment, the values of the activation energy and the reaction orders were calculated. The activation energy of the carbonate dissolution process, in kJ/mol, was as follows: 61.6 for cerium, 39.9 for neodymium, 45.4 for ytterbium. The apparent reaction orders of the carbonates are equal to one. The prospect of using the research results lies in the potential to create a mathematical model of the process of extracting a rare earth metal by the carbonate alkaline method.

Studying Drug Release through Polymeric Controlled Release Formulations in United States Pharmacopoeia 2 Apparatus Using Multiphysics Simulation and Experiments

In vitro dissolution of oral drug formulations is often studied using the United States Pharmacopoeia (USP) apparatus. Although a well-stirred vessel or a perfect sink assumption is often employed in the modeling of in vitro dissolution in USP apparatus, such a limit is usually not realized in actual experimental conditions. The interplay of hydrodynamics in the vessel and the swelling and erosion of dosage forms often results in substantial deviations from the dissolution behavior obtained under perfect sink approximation. We develop a multiphysics model of drug release from controlled release tablets of polymeric excipients with active pharmaceutical ingredients (APIs). Simulations are performed in COMSOL for the USP 2 (paddle) apparatus and the effects of stirring speed, drug loading, erosion rate, and polymer swelling and erosion are analyzed in detail. We demonstrate that the drug release phenomena can be conveniently interpreted using the Weibull equation to fit the simulation results. This is further confirmed using drug release experiments performed on mechanically compressed tablets of naproxen sodium as the API with poly-methyl-methacrylate-co-methacrylic acid as the excipient. We show that the API-to-polymer ratio may be varied to obtain different regimes of controlled release.

A moving-boundary model of dissolution from binary drug-excipient granules incorporating microstructure

Accurate mechanistic in vitro dissolution models can deliver insight into drug release behaviour and guide formulation development. Drug release profiles from drug-excipient granules can be impacted by variation of porosity and drug load within granules, which may arise from inherent variability in granulation processes. Here, we analyse and validate a recent model of drug release from a single spherical granule with a matrix of insoluble excipient, incorporating radial variation of porosity and drug load. The model is presented and specialised to the case where the initial drug load is large compared to the capacity of the granule's pores at solubility. In this limit, the model reduces to a single ordinary differential equation describing depletion of a shrinking, drug-saturated core. Model validation is performed using drug release data from the literature for a granule system consisting of acetaminophen and microcrystalline cellulose. A new extended model to describe dissolution from a polydisperse collection of granules is derived. The performance is compared to single particle models using equivalent spherical diameters. The developed model provides a new tool to explore the dissolution parameter space for these systems and for considering the impact of radial variation of granule porosity and drug load arising from manufacturing processes.

Dissolution Kinetics of a BCS Class II Active Pharmaceutical Ingredient: Diffusion-Based Model Validation and Prediction

In this work, a diffusion-theory-based model has been devised to simulate dissolution kinetics of a poorly water-soluble drug, ibuprofen. The model was developed from the Noyes-Whitney equation in which the dissolution rate term is a function of the remaining particulate surface area and the concentration gradient across the boundary layer. Other dissolution parameters include initial particle size, diffusion coefficient, material density, and diffusion boundary layer thickness. It is useful for predicting nonsink circumstances under which pure API polydisperse powders are suspended in a well-mixing tank. The model was used to compare the accuracy of simulations using spherical (single dimensional characteristic length) and cylindrical particle (multidimensional characteristic lengths) geometries, with and without size-dependent diffusion layer thickness. Experimental data was fitted to the model to obtain the diffusion layer thickness as well as used for model validation and prediction. The CSDs of postdissolution were also predicted with this model, demonstrating good agreement between theory and experiment.

Hierarchical Mass Transfer Analysis of Drug Particle Dissolution, Highlighting the Hydrodynamics, pH, Particle Size, and Buffer Effects for the Dissolution of Ionizable and Nonionizable Drugs in a Compendial Dissolution Vessel

Dissolution is a crucial process for the oral delivery of drug products. Before being absorbed through epithelial cell membranes to reach the systemic circulation, drugs must first dissolve in the human gastrointestinal (GI) tract. In vivo and in vitro dissolutions are complex because of their dependency upon the drug physicochemical properties, drug product, and GI physiological properties. However, an understanding of this process is critical for the development of robust drug products. To enhance our understanding of in vivo and in vitro dissolutions, a hierarchical mass transfer (HMT) model was developed that considers the drug properties, GI fluid properties, and fluid hydrodynamics. The key drug properties include intrinsic solubility, acid/base character, pK_a, particle size, and particle polydispersity. The GI fluid properties include bulk pH, buffer species concentration, fluid shear rate, and fluid convection. To corroborate the model, in vitro dissolution experiments were conducted in the United States Pharmacopeia (USP) 2 dissolution apparatus. A weakly acidic (ibuprofen), a weakly basic (haloperidol), and a nonionizable (felodipine) drug were used to study the effects of the acid/base character, pK_a, and intrinsic solubility on dissolution. 900 mL of 5 mM bicarbonate and phosphate buffers at pH 6.5 and 37 °C was used to study the impact of the buffer species on drug dissolution. To investigate the impacts of fluid shear rate and convection, the apparatus was operated at different impeller rotational speeds. Moreover, presieved ibuprofen particles with different average diameters were used to investigate the effect of particle size on drug dissolution. In vitro experiments demonstrate that the dissolution rates of both the ionizable compounds used in this study were slower in bicarbonate buffer than in phosphate buffer, with the same buffer concentration, because of the lower interfacial buffer capacity, a unique behavior of bicarbonate buffer. Therefore, using surrogates (i.e., 50 mM phosphate) for bicarbonate buffer for biorelevant in vitro dissolution testing may overestimate the in vivo dissolution rate for ionizable drugs. Model simulations demonstrated that, assuming a monodisperse particle size when modeling, dissolution may overestimate the dissolution rate for polydisperse particle size distributions. The hydrodynamic parameters (maximum shear rate and fluid velocity) under in vitro conditions in the USP 2 apparatus under different rotational speeds are orders of magnitude higher compared to the in vivo situation. The inconsistencies between the in vivo and in vitro drug dissolution hydrodynamic conditions may cause an overestimation of the dissolution rate under in vitro conditions. The in vitro dissolution data supported the accuracy of the HMT for drug dissolution. This is the first drug dissolution model that incorporates the effect of the bulk pH and buffer concentration on the interfacial drug particle solubility of ionizable compounds, combined with the medium hydrodynamics effect (diffusion, convection, shear, and confinement components), and drug particle size distribution.

Selection of In Vivo Predictive Dissolution Media Using Drug Substance and Physiological Properties

The rate and extent of drug dissolution in the gastrointestinal (GI) tract are highly dependent upon drug physicochemical properties and GI fluid properties. Biorelevant dissolution media (BDM), which aim to facilitate in vitro prediction of in vivo dissolution performance, have evolved with our understanding of GI physiology. However, BDM with a variety of properties and compositions are available, making the choice of dissolution medium challenging. In this tutorial, we describe a simple and quantitative methodology for selecting practical, yet physiologically relevant BDM representative of fasted humans for evaluating dissolution of immediate release formulations. Specifically, this methodology describes selection of pH, buffer species, and concentration and evaluates the importance of including bile salts and phospholipids in the BDM based upon drug substance log D, pK_a, and intrinsic solubility. The methodology is based upon a mechanistic understanding of how three main factors affect dissolution, including (1) drug ionization at gastrointestinal pH, (2) alteration of surface pH by charged drug species, and (3) drug solubilization in mixed lipidic aggregates comprising bile salts and phospholipids. Assessment of this methodology through testing and comparison with literature reports showed that the recommendations correctly identified when a biorelevant buffer capacity or the addition of bile salts and phospholipids to the medium would appreciably change the drug dissolution profile. This methodology can enable informed decisions about when a time, complexity, and/or cost-saving buffer is expected to lead to physiologically meaningful in vitro dissolution testing, versus when a more complex buffer would be required.

Biorelevant intrinsic dissolution profiling in early drug development: Fundamental, methodological, and industrial aspects

Intrinsic dissolution rate (IDR) is the surface specific dissolution rate of a drug. In early drug development, this property (among other parameters) is measured in order to compare different polymorphs and salt forms, guide formulation decisions, and to provide a quality marker of the active pharmaceutical ingredient (API) during production. In this review, an update on different methods and small-scale techniques that have recently evolved for determination of IDR is provided. The importance of biorelevant media and the hydrodynamic conditions of dissolution are also discussed. Different preparation techniques for samples are presented with a focus on disc, particle- and crystal-based methods. A number of small-scale techniques are then described in detail, and their applicability domains are identified. Finally, an updated industrial perspective is provided about IDR's place in the early drug development process.

First-Principles and Empirical Approaches to Predicting In Vitro Dissolution for Pharmaceutical Formulation and Process Development and for Product Release Testing

This manuscript represents the perspective of the Dissolution Working Group of the International Consortium for Innovation and Quality in Pharmaceutical Development (IQ) and of two focus groups of the American Association of Pharmaceutical Scientists (AAPS): Process Analytical Technology (PAT) and In Vitro Release and Dissolution Testing (IVRDT). The intent of this manuscript is to show recent progress in the field of in vitro predictive dissolution modeling and to provide recommended general approaches to developing in vitro predictive dissolution models for both early- and late-stage formulation/process development and batch release. Different modeling approaches should be used at different stages of drug development based on product and process understanding available at those stages. Two industry case studies of current approaches used for modeling tablet dissolution are presented. These include examples of predictive model use for product development within the space explored during formulation and process optimization, as well as of dissolution models as surrogate tests in a regulatory filing. A review of an industry example of developing a dissolution model for real-time release testing (RTRt) and of academic case studies of enabling dissolution RTRt by near-infrared spectroscopy (NIRS) is also provided. These demonstrate multiple approaches for developing data-rich empirical models in the context of science- and risk-based process development to predict in vitro dissolution. Recommendations of modeling best practices are made, focused primarily on immediate-release (IR) oral delivery products for new drug applications. A general roadmap is presented for implementation of dissolution modeling for enhanced product understanding, robust control strategy, batch release testing, and flexibility toward post-approval changes.

Strontium-containing, carbohydrate-based polymer networks as tooth-adherent systems for the treatment of dentine hypersensitivity

This study describes the design/physicochemical properties of strontium-containing, mucoadhesive carbohydrate polymeric platforms, designed as treatments for dentine hypersensitivity. Interactive networks were composed of strontium chloride (10% w/w), one of two base polymers (sodium carboxymethylcellulose, NaCMC or hydroxyethylcellulose, HEC), polycarbophil (PC) and, when required, polyvinylpyrrolidone (PVP). The physicochemical properties were characterised using oscillatory and flow rheometry, texture profile analysis, mucoadhesion analysis and, additionally, the strontium release properties were examined. All platforms exhibited pseudoplastic flow. Increasing polymer concentrations increased network viscoelasticity, consistency, hardness, compressibility, gel strength, adhesiveness, mucoadhesion and, retarded strontium release. Principally zero-order strontium release was observed from all platforms. Incorporation of strontium reduced the network elasticity, consistency, hardness, compressibility, gel strength and mucoadhesion; HEC-based platforms being affected to a greater extent than NaCMC platforms. NaCMC-based platforms containing 10% strontium chloride, PVP (3% w/w) and PC (3% w/w) potentially displayed the correct balance of physicochemical properties for the treatment of dentine sensitivity.